prior_predictive_check

library load

library(tidyverse)

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library(glue)
library(tidybayes)
library(cowplot)

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library(scales)

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library(GGally)

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library(knitr)
library(matrixStats)

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theme_set(theme_cowplot())

load_existing_sim <- TRUE

A slight change from m1 in where the group pre mean for circSD is located. Done to shift probability away from extreme circSD values > 100

model

Written down the model is:

\[ \begin{aligned} \mathrm{-likelihood-} \\ error_i &\sim (pMem_i)*VM(0, \kappa_i) + (1 - pMem_i)*Unif(-\pi,\pi) \\ \\ \mathrm{-param~transformation-} \\ \kappa_i &= sd2k(circ\_sd_i) \\ \\ \mathrm{-linear~model-} \\ circ\_sd_i &= exp(\alpha_{0,SUBJ[i]} + \alpha_{\Delta,SUBJ[i]} * postCond) ~~ \mathrm{-log~link~on~circSD-} \\ pMem_i &= inv\_logit(\beta_{0,SUBJ[i]} + \beta_{\Delta,SUBJ[i]} * postCond) ~~ \mathrm{-logit~link~on~pMem-} \\ \\ \mathrm{-priors:~all~independent-}\\ \alpha_{0,SUBJ[...]} &\sim Normal(mu\_\alpha_0, sigma\_\alpha_0) \\ \alpha_{\Delta,SUBJ[...]} &\sim Normal(mu\_\alpha_{\Delta}, sigma\_\alpha_{\Delta}) \\ \beta_{0,SUBJ[...]} &\sim Normal(mu\_\beta_0, sigma\_\beta_0) \\ \beta_{\Delta,SUBJ[...]} &\sim Normal(mu\_\beta_{\Delta}, sigma\_\beta_{\Delta}) \\ \\ mu\_\alpha_0 &\sim Normal(3.8, 0.5)\\ sigma\_\alpha_0 &\sim Normal^+(0, 0.5) \\ mu\_\alpha_{\Delta} &\sim Normal(0, 0.5)\\ sigma\_\alpha_{\Delta} &\sim Normal^+(0, 0.5)\\ mu\_\beta_0 &\sim Normal(0, 1.5)\\ sigma\_\beta_0 &\sim Normal^+(0, 1.5)\\ mu\_\beta_{\Delta} &\sim Normal(0, 1)\\ sigma\_\beta_{\Delta} &\sim Normal^+(0, 1)\\ \\ \\ \\ \mathrm{-model~changes~from~m1-}\\ mu\_\alpha_0 \sim Normal(4, 0.5) ~~ ...~&to~... ~~ mu\_\alpha_0 \sim Normal(3.8, 0.5) \\ \end{aligned} \]

---

real obs load

I am considering the color stimulation data. samples sizes:

obs_data <- read_csv(glue('{params$model_dir_str}/data/stimulation_obvs.csv'))

## Parsed with column specification:
## cols(
##   subj = col_double(),
##   subj_index = col_double(),
##   stimulation = col_double(),
##   error = col_double()
## )

#summarize subj num, obs count, and obs condition split
(subj_summary <- obs_data %>%
  group_by(subj_index) %>%
  summarise(n_obs = n(), frac_stim = mean(stimulation)))

## # A tibble: 2 x 3
##   subj_index n_obs frac_stim
##        <dbl> <int>     <dbl>
## 1          1   252       0.5
## 2          2   252       0.5

2 subjs with 252 observations each, 126 per condition.

9/12 - I am thinking I should simulate varying effects using the actual samples sizes I have. I also think that this shouldnt matter (at least for a model like this). I’ll also try with a larger number of subjects.

---

Simulation

functions

source(glue("{params$common_dir_str}/simulation.R"))

run simulate

here the idea is to take the priors and simulate many possible data sets from them. Since this is a two-level multilevel model, there are three steps of stimulation. First simulate from the group-level priors, then for each draw from the group-level params, simulate a number of subjects (in the case set as a constant value for all simulations), and lastly within each subject simulate observations/responses during the task (in this case the nobs_per_cond is also set as fixed for all simulations).

source(glue("{params$model_dir_str}/model_prior.R"))

## Loading required package: brms

## Loading required package: Rcpp

## Loading 'brms' package (version 2.10.3). Useful instructions
## can be found by typing help('brms'). A more detailed introduction
## to the package is available through vignette('brms_overview').

print(bprior_full)

##              prior class        coef group resp   dpar nlpar bound
## 1 normal(3.8, 0.5)     b   intercept            circSD            
## 2   normal(0, 0.5)     b stimulation            circSD            
## 3   normal(0, 0.5)    sd   Intercept  subj      circSD            
## 4   normal(0, 0.5)    sd stimulation  subj      circSD            
## 5   normal(0, 1.5)     b   intercept             theta            
## 6   normal(0, 1.5)     b stimulation             theta            
## 7     normal(0, 1)    sd   Intercept  subj       theta            
## 8     normal(0, 1)    sd stimulation  subj       theta

conditions <- c(0,1)

sim_datasets_fpath <- glue("{params$save_dir_str}/sim_datasets.rds")

found_existing_sim <- FALSE
if (file.exists(sim_datasets_fpath)){
  found_existing_sim <- TRUE
}


if (load_existing_sim == FALSE || found_existing_sim == FALSE){

  print("simulating")
  
  nsim_datasets <- 2000
  nsubj_sim <- 15
  nobs_per_cond_sim <- 1500

  # this generates a data frame with one column for each group level variable that is sampled
  # it also contains a simulation index (sim_num), number of subjects to simulate in each dataset,
  # and the number of observations we have from each subject per condition
  sim_priors <- tibble(
    sim_num = 1:nsim_datasets,
    alpha0_mu = rnorm(nsim_datasets, alpha0_mu_prior_mu, alpha0_mu_prior_sd),
    alpha0_sigma = abs(rnorm(nsim_datasets, alpha0_sigma_prior_mu, alpha0_sigma_prior_sd)),
    alphaD_mu =  rnorm(nsim_datasets, alphaD_mu_prior_mu, alphaD_mu_prior_sd),
    alphaD_sigma = abs(rnorm(nsim_datasets, alphaD_sigma_prior_mu, alphaD_sigma_prior_sd)),
    beta0_mu = rnorm(nsim_datasets, beta0_mu_prior_mu, beta0_mu_prior_sd),
    beta0_sigma = abs(rnorm(nsim_datasets, beta0_sigma_prior_mu, beta0_sigma_prior_sd)),
    betaD_mu = rnorm(nsim_datasets, betaD_mu_prior_mu, betaD_mu_prior_sd),
    betaD_sigma = abs(rnorm(nsim_datasets, betaD_sigma_prior_mu, betaD_sigma_prior_sd)),
    nsubj = nsubj_sim,
    nobs_per_cond = nobs_per_cond_sim
  )
  
  # using those simulated group-level priors, next simulate subjects and observations from those subjects.
  sim_datasets <- 
    sim_priors %>%
    mutate(
      # use draw_subj to sample nsubj_sim per sim using group-level parameter draws
      dataset = pmap(sim_priors, draw_subj),
      stimulation = list(stimulation = rep(conditions, each = nobs_per_cond_sim))) %>%
    
    # first unnest dataset, expanding by nsubj_sim and copying stimulation list to each subj
    unnest(dataset) %>%
    
    # then unnest stimulation, expanding by nobs_per_cond_sim*2
    unnest(stimulation) %>%
    
    # now use likelihood to simulation observations
    mutate(
      # evaluate and delink linear model on pMem
      pMem = inv_logit(subj_beta0 + (subj_betaD * stimulation)),
      
      # evaluate and delink linear model on circSD/kappa
      k = sd2k_vec(
        pracma::deg2rad(
          exp(subj_alpha0 + (subj_alphaD * stimulation)))),
      
      # use pMem to draw a 1 or 0 for each trial
      memFlip = rbernoulli(n(), pMem),
      
      # use k to draw from vonMises for each trial
      vm_draw = rvonmises_vec(1, pi, k) - pi,
      
      # draw from unif for each trial
      unif_draw = runif(n(), -pi, pi),
      
      # assign either vm_draw or unif_draw to each trial, depending on memFlip
      obs_radian = memFlip * vm_draw + (1 - memFlip) * unif_draw,
      
      # convert to degrees
      obs_degree = obs_radian * (180/pi)
    ) %>%
    select(-c(pMem, k, memFlip, vm_draw, unif_draw)) %>%
    nest(subj_obs = c(stimulation, obs_degree, obs_radian)) %>%
    nest(dataset = c(subj, subj_alpha0, subj_alphaD, subj_beta0, subj_betaD, nobs_per_condition, subj_obs))

  
  saveRDS(sim_datasets, file = sim_datasets_fpath)

}else{
  
  sim_datasets <- readRDS(sim_datasets_fpath)
}

nsim_datasets <- nrow(sim_datasets)
nsubj_sim <- sim_datasets$nsubj[1]
nobs_per_cond_sim <- sim_datasets$nobs_per_cond[1] 

Check sim data

head(sim_datasets)

## # A tibble: 6 x 12
##   sim_num alpha0_mu alpha0_sigma alphaD_mu alphaD_sigma beta0_mu
##     <int>     <dbl>        <dbl>     <dbl>        <dbl>    <dbl>
## 1       1      4.31       1.02     -0.208         0.556   -0.846
## 2       2      3.77       0.197     0.901         0.500   -0.389
## 3       3      2.84       0.408    -1.19          0.823   -1.06 
## 4       4      3.53       0.406    -0.452         0.491   -0.589
## 5       5      4.06       0.402     0.0420        0.682   -1.07 
## 6       6      3.28       0.0563    0.626         0.919   -1.17 
## # … with 6 more variables: beta0_sigma <dbl>, betaD_mu <dbl>,
## #   betaD_sigma <dbl>, nsubj <dbl>, nobs_per_cond <dbl>, dataset <S3:
## #   vctrs_list_of>

head(sim_datasets$dataset[[1]])

## # A tibble: 6 x 7
##    subj subj_alpha0 subj_alphaD subj_beta0 subj_betaD nobs_per_condit…
##   <int>       <dbl>       <dbl>      <dbl>      <dbl>            <dbl>
## 1     1        3.71      -0.118     -0.920    -1.28               1500
## 2     2        5.04      -0.393     -0.709     0.943              1500
## 3     3        4.20      -0.224     -0.904     1.05               1500
## 4     4        4.12      -0.726     -1.03      1.18               1500
## 5     5        2.35       0.205     -0.640     0.346              1500
## 6     6        3.90      -0.180     -0.737    -0.0899             1500
## # … with 1 more variable: subj_obs <S3: vctrs_list_of>

head(sim_datasets$dataset[[1]]$subj_obs[[1]])

## # A tibble: 6 x 3
##   stimulation obs_degree obs_radian
##         <dbl>      <dbl>      <dbl>
## 1           0     -47.2      -0.824
## 2           0    -149.       -2.60 
## 3           0       6.56      0.115
## 4           0     -45.1      -0.787
## 5           0     -16.2      -0.283
## 6           0      31.9       0.557

---

Plot distributions and summary statistics

Ideas:

Definitely plot the priors on the intercept and slope means, transformed back into sd

plot the prior predicitive densities for subjects

Some other plot ideas:

shaded histogram plot, combining data across stimulation conditions - check if data looks too peaked or too flat

shaded histogram plot, one for each stimulation condition - same check ^

plot of density lines, one from each sim dataset, one with both conditions and one with them split out - this would help identify weird distribution more that shaded histogram perhaps

Correctness checks that prior samples are drawn correctly

sim_datasets %>%
  select(alpha0_mu, alpha0_sigma, alphaD_mu, alphaD_sigma) %>%
  ggpairs(progress = FALSE)

sim_datasets %>%
  select(beta0_mu, beta0_sigma, betaD_mu, betaD_sigma) %>%
  ggpairs(progress = FALSE)

Correctness check of likelihood simulation

This code simulates distributions of oberservations using the mixture likelihood, sweeping across parameter combos.

param_set <- cross_df(list(pMem = seq(0, 1, 0.1), sd = seq(20, 50, 5)))

param_set %>%
  mutate(sims = map2(param_set$pMem, sd2k_vec(pracma::deg2rad(param_set$sd)), ~simulateData_likelihood(.x, .y, 1000))) %>%
  unnest(sims) %>% 
  ggplot(aes(x = obs_degree)) + 
  geom_histogram(binwidth = 1) +
  facet_grid(rows = vars(pMem), cols = vars(sd), labeller = 'label_both', scales = 'free')

param_set <- cross_df(list(pMem = seq(0, 1, 0.1), sd = seq(55, 105, 5)))

param_set %>%
  mutate(sims = map2(param_set$pMem, sd2k_vec(pracma::deg2rad(param_set$sd)), ~simulateData_likelihood(.x, .y, 1000))) %>%
  unnest(sims) %>% 
  ggplot(aes(x = obs_degree)) + 
  geom_histogram(binwidth = 1)+
  facet_grid(rows = vars(pMem), cols = vars(sd), labeller = 'label_both')

* Notes

all good

---

Prior distribution on von-mises circSD, linear model parameters

(pre group mean, post group mean, post-pre mean change)

No accounting for group-level variance here

##
## alpha0_mu 
##

## linked prior distribution
alpha0_mu_hist <- sim_datasets %>%
  ggplot(aes(x = alpha0_mu)) + 
  geom_histogram(binwidth = 0.05, fill = "#F16C66") +
  theme(legend.position = "none",
        axis.title = element_text(size = 12),
        plot.title = element_text(size = 12)) + 
  labs(x = "linked prior on group mean for circSD, pre condition",
       title = "circSD group mean prior, alpha0_mu") + 
  scale_x_continuous(limits = c(1,7))
  

##
## alpha0_mu + alphaD_mu = alpha1_mu 
##

## linked prior distribution
alpha1_mu_hist <- sim_datasets %>%
  transmute(alpha1_mu = alpha0_mu + alphaD_mu) %>%
  ggplot(aes(x = alpha1_mu)) + 
  geom_histogram(binwidth = 0.05, fill = "#685369") +
  theme(axis.title = element_text(size = 12),
        plot.title = element_text(size = 12)) +
  labs(x = "linked prior on group mean for circSD, post condition",
       title = "circSD group mean prior, alpha0_mu + alphaD_mu") + 
  scale_x_continuous(limits = c(1,7))


plot_grid(alpha0_mu_hist, alpha1_mu_hist, nrow = 1, align = "h")

## Warning: Removed 2 rows containing missing values (geom_bar).

## Warning: Removed 2 rows containing missing values (geom_bar).

##
## alpha0_mu 
##

## delinked prior alpha0_mu
alpha0_mu_delinked_stats <- sim_datasets %>%
  transmute(delinked = exp(alpha0_mu)) %>%
  summarise(less_than_5 = sum(delinked < 5)/n(), greater_than_120 = sum(delinked > 120)/n())

alpha0_mu_delinked_hist <- sim_datasets %>%
  transmute(delinked = exp(alpha0_mu)) %>%
  ggplot(aes(x = delinked)) +
  geom_histogram(binwidth = 2, fill = "#F16C66") + 
  geom_vline(xintercept = c(5, 120), linetype = "dashed") + 
  labs(x = "prior on group mean for circSD, pre condition",
       title = "circSD group mean prior, exp(alpha0_mu)",
       subtitle = glue("prob(circSD < 5) = {alpha0_mu_delinked_stats$less_than_5}\nprob(circSD > 120) = {alpha0_mu_delinked_stats$greater_than_120}")) + 
  theme(axis.title = element_text(size = 12),
        plot.title = element_text(size = 12)) 
  
##
## alpha0_mu + alphaD_mu = alpha1_mu 
##  
  
## delinked prior alpha0_mu + alphaD_mu
alpha1_mu_delinked_hist <- sim_datasets %>%
  transmute(delinked = exp(alpha0_mu + alphaD_mu)) %>%
  ggplot(aes(x = delinked)) + 
  geom_histogram(binwidth = 2, fill = "#685369") + 
  labs(x = "prior on group mean for circSD, post condition",
       title = "circSD group mean prior, exp(alpha0_mu + alphaD_mu)") + 
  theme(axis.title = element_text(size = 12),
        plot.title = element_text(size = 12))


plot_grid(alpha0_mu_delinked_hist, alpha1_mu_delinked_hist, nrow = 1, align = "h")

##
## exp(alpha0_mu + alphaD_mu) - exp(alpha0_mu) plot
##

alphaD_mu_delinked_stats <- sim_datasets %>%
  transmute(delinked = exp(alpha0_mu + alphaD_mu) - exp(alpha0_mu)) %>%
  summarise(less_than_n100 = sum(delinked < -100)/n(), greater_than_100 = sum(delinked > 100)/n())

alphaD_mu_delinked_hist <- sim_datasets %>%
  transmute(delinked = exp(alpha0_mu + alphaD_mu) - exp(alpha0_mu)) %>%
  ggplot(aes(x = delinked)) + 
  geom_histogram(binwidth = 2, fill = "#00AEB2") + 
  geom_vline(xintercept = c(-100, 100), linetype = "dashed") + 
  labs(x = "prior on group mean for delta-circSD, mean post minus mean pre",
       title = "delta-circSD group mean prior, exp(alpha0_mu + alphaD_mu) - exp(alpha0_mu)",
       subtitle = glue("prob(delta-circSD < -100) = {alphaD_mu_delinked_stats$less_than_n100}\nprob(delta-circSD > 100) = {alphaD_mu_delinked_stats$greater_than_100}")) + 
  theme(axis.title = element_text(size = 12),
        plot.title = element_text(size = 12)) + 
  scale_x_continuous(breaks= pretty_breaks(10))

alphaD_mu_delinked_hist

* Notes

Definitely better containment of the group circSD means

---

Prior predicitive distribution on circSD at the subject level

(based on simulated subjects from each dataset)

These plots indicate the effects of the priors on alpha0_mu, alpha0_sigma, alphaD_mu, alphaD_sigma.

Marginal prior on subjects pre circSD, post circSD, and effect size

using only one simulated subject per dataset (ignoring simulation sample sizes)

sim_datasets_unnest <- sim_datasets %>%
  unnest(dataset) %>%
  mutate(alpha0_mu_delinked = exp(alpha0_mu),
         alpha1_mu_delinked = exp(alpha0_mu + alphaD_mu),
         subj_pre_circSD = exp(subj_alpha0),
         subj_post_circSD = exp(subj_alphaD + subj_alpha0),
         subj_circSD_ES = subj_post_circSD - subj_pre_circSD) 

subj_pre_circSD_plot <- sim_datasets_unnest %>%
  mutate(subj_pre_circSD = if_else(subj_pre_circSD > 120, 120, subj_pre_circSD)) %>%
  group_by(sim_num) %>%
  sample_n(1) %>%
  ungroup() %>%
  ggplot(aes(x = subj_pre_circSD)) + 
  geom_histogram(binwidth = 5, fill = "red", alpha = 0.3) + 
  labs(x = "subj_pre_circSD [prior predictive distribution]",
       subtitle = glue("p(<5) = {sum(sim_datasets_unnest$subj_pre_circSD < 5)/length(sim_datasets_unnest$subj_pre_circSD)}\n p(>120) = {sum(sim_datasets_unnest$subj_pre_circSD > 120)/length(sim_datasets_unnest$subj_pre_circSD)}"))


subj_post_circSD_plot <- sim_datasets_unnest %>%
  mutate(subj_post_circSD = if_else(subj_post_circSD > 120, 120, subj_post_circSD)) %>%
  group_by(sim_num) %>%
  sample_n(1) %>%
  ungroup() %>%
  ggplot(aes(x = subj_post_circSD)) + 
  geom_histogram(binwidth = 5, fill = "red", alpha = 0.3) + 
  labs(x = "subj_post_circSD [prior predictive distribution]",
       subtitle = glue("p(<5) = {sum(sim_datasets_unnest$subj_post_circSD < 5)/length(sim_datasets_unnest$subj_post_circSD)}\n p(>120) = {sum(sim_datasets_unnest$subj_post_circSD > 120)/length(sim_datasets_unnest$subj_post_circSD)}"))


subj_circSD_ES_plot <- sim_datasets_unnest %>%
  mutate(subj_circSD_ES = if_else(subj_circSD_ES > 100, 100, subj_circSD_ES)) %>%
  mutate(subj_circSD_ES = if_else(subj_circSD_ES < -100, -100, subj_circSD_ES)) %>%
  group_by(sim_num) %>%
  sample_n(1) %>%
  ungroup() %>%
  ggplot(aes(x = subj_circSD_ES)) + 
  geom_histogram(binwidth = 5, fill = "red", alpha = 0.7) + 
  labs(x = "subj_circSD_ES [prior predictive distribution]",
       subtitle = glue("p(< -100) = {sum(sim_datasets_unnest$subj_circSD_ES < -100)/length(sim_datasets_unnest$subj_circSD_ES)}\n p(>100) = {sum(sim_datasets_unnest$subj_circSD_ES > 100)/length(sim_datasets_unnest$subj_circSD_ES)}"))

plot_grid(subj_pre_circSD_plot, subj_post_circSD_plot, subj_circSD_ES_plot, ncol = 1)

Calculate min and max subject pre, post, and circSD effect size in each simulation.

sim_subj_extremes <- sim_datasets %>% 
  unnest(dataset) %>%
  mutate(subj_alpha1 = subj_alpha0 + subj_alphaD, 
         subj_alpha0_delinked = exp(subj_alpha0), 
         subj_alpha1_delinked = exp(subj_alpha1), 
         subj_circSD_effect = subj_alpha1_delinked - subj_alpha0_delinked ) %>%
  group_by(sim_num) %>%
  summarize_at(vars(subj_alpha0_delinked, subj_alpha1_delinked, subj_circSD_effect), list(max = max, min = min)) 

Across-sim SD of circSD

This is done to get a sense of the effect of group-level variance priors. I am doing it this way (estimating sd among subjects after simulation) because it not straightforward to tranform variance in the log space to variance after exponentiating.

simSD <- sim_datasets %>% 
  unnest(dataset) %>%
  mutate(subj_pre_circSD = exp(subj_alpha0),
         subj_post_circSD = exp(subj_alpha0 + subj_alphaD)) %>%
  group_by(sim_num) %>%
  summarise_at(vars(subj_pre_circSD, subj_post_circSD), list(mean = mean, sd = sd))

plot_grid(
  
  ggplot(simSD, aes(subj_pre_circSD_sd)) + 
    geom_histogram(binwidth = 2) + 
    xlim(0, 200) + 
    labs(x = "pre condition: observed SD of distribution of circSD, per sim", 
         subtitle = glue::glue("p(>50) = {mean(simSD$subj_pre_circSD_sd > 50)}")),
  
  ggplot(simSD, aes(subj_post_circSD_sd)) + 
    geom_histogram(binwidth = 2) +
    xlim(0, 200) + 
    labs(x = "post condition: observed SD of distribution of circSD, per sim",
        subtitle = glue::glue("p(>50) = {mean(simSD$subj_post_circSD_sd > 50)}")),
  
  ncol = 1
  )                                                             

## Warning: Removed 30 rows containing non-finite values (stat_bin).

## Warning: Removed 2 rows containing missing values (geom_bar).

## Warning: Removed 92 rows containing non-finite values (stat_bin).

## Warning: Removed 2 rows containing missing values (geom_bar).

plot_grid(
  
  ggplot(simSD, aes(subj_pre_circSD_mean, subj_pre_circSD_sd)) + 
    geom_point() + 
    xlim(0, 200) + ylim(0, 100) + 
    labs(x = "pre condition: observed mean of distribution of circSD, per sim",
         y = "pre condition: observed sd"),
  
  ggplot(simSD, aes(subj_post_circSD_mean, subj_post_circSD_sd)) + 
    geom_point() +
    xlim(0, 200) + ylim(0, 100) + 
    labs(x = "post condition: observed mean of distribution of circSD, per sim",
         y = "post condition: observed sd"),
  
  ncol = 1
  )                                                             

## Warning: Removed 100 rows containing missing values (geom_point).

## Warning: Removed 301 rows containing missing values (geom_point).

Across-sim max circSD

This is done to get a sense if the max/min in each dataset are consistently too extreme.

#What is the max subject pre condition value in each dataset
pre_plot <- sim_subj_extremes %>%
  mutate(subj_alpha0_delinked_max = if_else(subj_alpha0_delinked_max > 120, 120, subj_alpha0_delinked_max)) %>%
  ggplot() + 
  geom_histogram(aes(x = subj_alpha0_delinked_max, fill = "red", alpha = 0.3), binwidth = 5) +
  theme(legend.position = "none") + 
  labs(x = "pre condition: max subj circSD per sim [subj_alpha0_delinked_max]",
       subtitle = glue("p(<5) = {sum(sim_subj_extremes$subj_alpha0_delinked_max < 5)/length(sim_subj_extremes$subj_alpha0_delinked_max)}\n p(>120) = {sum(sim_subj_extremes$subj_alpha0_delinked_max > 120)/length(sim_subj_extremes$subj_alpha0_delinked_max)}"))

#What is the max subject post condition value in each dataset
post_plot <- sim_subj_extremes %>%
  mutate(subj_alpha1_delinked_max = if_else(subj_alpha1_delinked_max > 120, 120, subj_alpha1_delinked_max)) %>%
  ggplot() + 
  geom_histogram(aes(x = subj_alpha1_delinked_max, fill = "red", alpha = 0.3), binwidth = 5) + 
  theme(legend.position = "none") + 
  labs(x = "post condition: max subj circSD per sim [subj_alpha1_delinked_max]",
       subtitle = glue("p(<5) = {sum(sim_subj_extremes$subj_alpha1_delinked_max < 5)/length(sim_subj_extremes$subj_alpha1_delinked_max)}\n p(>120) = {sum(sim_subj_extremes$subj_alpha1_delinked_max > 120)/length(sim_subj_extremes$subj_alpha1_delinked_max)}"))


plot_grid(pre_plot, post_plot, ncol =1, align = 'v')

Across-sim min circSD

pre_plot <- sim_subj_extremes %>%
  mutate(subj_alpha0_delinked_min = if_else(subj_alpha0_delinked_min > 120, 120, subj_alpha0_delinked_min)) %>%
  ggplot() + 
  geom_histogram(aes(x = subj_alpha0_delinked_min, fill = "red", alpha = 0.3), binwidth = 5) +
  theme(legend.position = "none") + 
  labs(x = "pre condition: min subj circSD per sim [subj_alpha0_delinked_min]",
       subtitle = glue("p(<5) = {sum(sim_subj_extremes$subj_alpha0_delinked_min < 5)/length(sim_subj_extremes$subj_alpha0_delinked_min)}\n p(>120) = {sum(sim_subj_extremes$subj_alpha0_delinked_min > 120)/length(sim_subj_extremes$subj_alpha0_delinked_min)}"))

#What is the most extreme subject post condition value in each dataset
post_plot <- sim_subj_extremes %>%
  mutate(subj_alpha1_delinked_min = if_else(subj_alpha1_delinked_min > 120, 120, subj_alpha1_delinked_min)) %>%
  ggplot() + 
  geom_histogram(aes(x = subj_alpha1_delinked_min, fill = "red", alpha = 0.3), binwidth = 5) + 
  theme(legend.position = "none") + 
  labs(x = "post condition: min subj circSD per sim [subj_alpha1_delinked_min]",
       subtitle = glue("p(<5) = {sum(sim_subj_extremes$subj_alpha1_delinked_min < 5)/length(sim_subj_extremes$subj_alpha1_delinked_min)}\n p(>120) = {sum(sim_subj_extremes$subj_alpha1_delinked_min > 120)/length(sim_subj_extremes$subj_alpha1_delinked_min)}"))


plot_grid(pre_plot, post_plot, ncol =1, align = 'v')

Across-sim max+min circSD effect size

#What is the most extreme change from pre to post in a subject

min_plot <- sim_subj_extremes %>%
  mutate(subj_circSD_effect_min = if_else(subj_circSD_effect_min > 100 , 100, subj_circSD_effect_min)) %>%
  mutate(subj_circSD_effect_min = if_else(subj_circSD_effect_min < -100 , -100, subj_circSD_effect_min)) %>%
  ggplot() + 
  geom_histogram(aes(x = subj_circSD_effect_min, fill = "red", alpha = 0.3), binwidth = 5) +
  theme(legend.position = "none") + 
  labs(x = "min subj circSD effect per sim \n[min(subj_alpha1_delinked - subj_alpha0_delinked)]",
       subtitle = glue("p(<-100) = {sum(sim_subj_extremes$subj_circSD_effect_min < -100)/length(sim_subj_extremes$subj_circSD_effect_min)}\n p(>100) = {sum(sim_subj_extremes$subj_circSD_effect_min > 100)/length(sim_subj_extremes$subj_circSD_effect_min)}"))

#What is the most extreme subject post condition value in each dataset
max_plot <- sim_subj_extremes %>%
  mutate(subj_circSD_effect_max = if_else(subj_circSD_effect_max > 100 , 100, subj_circSD_effect_max)) %>%
  mutate(subj_circSD_effect_max = if_else(subj_circSD_effect_max < -100 , -100, subj_circSD_effect_max)) %>%
  ggplot() + 
  geom_histogram(aes(x = subj_circSD_effect_max, fill = "red", alpha = 0.3), binwidth = 5) +
  theme(legend.position = "none") + 
  labs(x = "max subj circSD effect per sim \n[max(subj_alpha1_delinked - subj_alpha0_delinked)]",
       subtitle = glue("p(<-100) = {sum(sim_subj_extremes$subj_circSD_effect_max < -100)/length(sim_subj_extremes$subj_circSD_effect_max)}\n p(>100) = {sum(sim_subj_extremes$subj_circSD_effect_max > 100)/length(sim_subj_extremes$subj_circSD_effect_max)}"))

plot_grid(min_plot, max_plot, ncol =1, align = 'v')

* Notes

There could be less probability at extreme circSD values. Reducing this would likely be better done by reducing prior group SD.

Also, reducing prior group SD would also reduce extreme max values across subject sets.

---

Prior distribution on mixture probability pMem, linear model parameters

(pre group mean, post group mean, post-pre mean change)

## linked prior distribution


plot_grid(
  
  sim_datasets %>%
  ggplot(aes(x = beta0_mu)) + 
  geom_histogram(binwidth = 0.05, fill = "#F16C66") +
  theme(legend.position = "none",
        axis.title = element_text(size = 12),
        plot.title = element_text(size = 12)) + 
  labs(x = "linked prior on group mean for pMem, pre condition",
       title = "pMem group mean prior, beta0_mu") + 
  scale_x_continuous(limits = c(-5,5))
  
  ,
  
  sim_datasets %>%
  transmute(beta1_mu = beta0_mu + betaD_mu) %>%
  ggplot(aes(x = beta1_mu)) + 
  geom_histogram(binwidth = 0.05, fill = "#685369") +
  theme(axis.title = element_text(size = 12),
        plot.title = element_text(size = 12)) +
  labs(x = "linked prior on group mean for pMem, post condition",
       title = "pMem group mean prior, beta0_mu + betaD_mu") + 
  scale_x_continuous(limits = c(-5,5))
  
  ,
  
  nrow = 1,
  align = "h"
)

## Warning: Removed 3 rows containing non-finite values (stat_bin).

## Warning: Removed 2 rows containing missing values (geom_bar).

## Warning: Removed 35 rows containing non-finite values (stat_bin).

## Warning: Removed 2 rows containing missing values (geom_bar).

##
## inv_logit(beta0_mu)
##

##
## inv_logit(beta0_mu + betaD_mu) = inv_logit(beta1_mu) 
##  

## delinked prior alpha0_mu
beta0_mu_delinked_stats <- sim_datasets %>%
  transmute(delinked = exp(beta0_mu)/(exp(beta0_mu) + 1)) %>%
  summarise(less_than_5 = sum(delinked < 0.05)/n(), greater_than_95 = sum(delinked > 0.95)/n())

plot_grid(
  
  sim_datasets %>%
  transmute(delinked = exp(beta0_mu)/(exp(beta0_mu) + 1)) %>%
  ggplot(aes(x = delinked)) +
  geom_histogram(binwidth = 0.03, fill = "#F16C66") + 
  geom_vline(xintercept = c(0.05, 0.95), linetype = "dashed") + 
  labs(x = "prior on group mean for pMem, pre condition",
       title = "pMem group mean prior, inv_logit(beta0_mu)",
       subtitle = glue("prob(pMem < 0.05) = {beta0_mu_delinked_stats$less_than_5}\nprob(pMem > 0.95) = {beta0_mu_delinked_stats$greater_than_95}")) + 
  theme(axis.title = element_text(size = 12),
        plot.title = element_text(size = 12))
  
  ,
  
  sim_datasets %>%
  transmute(delinked = exp(beta0_mu + betaD_mu)/(exp(beta0_mu + betaD_mu) + 1)) %>%
  ggplot(aes(x = delinked)) + 
  geom_histogram(binwidth = 0.03, fill = "#685369") + 
  labs(x = "prior on group mean for pMem, post condition",
       title = "pMem group mean prior, inv_logit(alpha0_mu + alphaD_mu)") + 
  theme(axis.title = element_text(size = 12),
        plot.title = element_text(size = 12))
  
  ,
  
  nrow = 1,
  align = "h"
)

##
## inv_logit(beta0_mu + betaD_mu) - inv_logit(beta0_mu) plot
##

betaD_mu_delinked_stats <- sim_datasets %>%
  transmute(delinked = exp(beta0_mu + betaD_mu)/(exp(beta0_mu + betaD_mu) + 1) - exp(beta0_mu)/(exp(beta0_mu) + 1)) %>%
  summarise(less_than_n80 = sum(delinked < -0.8)/n(), greater_than_80 = sum(delinked > 0.8)/n())

sim_datasets %>%
  transmute(delinked = exp(beta0_mu + betaD_mu)/(exp(beta0_mu + betaD_mu) + 1) - exp(beta0_mu)/(exp(beta0_mu) + 1)) %>%
  ggplot(aes(x = delinked)) + 
  geom_histogram(binwidth = 0.02, fill = "#00AEB2") + 
  geom_vline(xintercept = c(-0.8, 0.8), linetype = "dashed") + 
  labs(x = "prior on group mean for delta-pMem, mean post minus mean pre",
       title = "delta-pMem group mean prior, inv_logit(beta0_mu + betaD_mu) - inv_logit(beta0_mu)",
       subtitle = glue("prob(delta-pMem < -0.8) = {betaD_mu_delinked_stats$less_than_n80}\nprob(delta-pMem > 0.8) = {betaD_mu_delinked_stats$greater_than_80}")) + 
  theme(axis.title = element_text(size = 12),
        plot.title = element_text(size = 12)) + 
  scale_x_continuous(breaks= pretty_breaks(10))

* Notes

no changes from m1 here, mean looks fine + uniformative.

---

Prior predicitive distribution of pMem at the subject level

(based on simulated subjects from each dataset)

Marginal prior on subjects pre pMem, post pMem, and effect size

using only one simulated subject per dataset (ignoring simulation sample sizes)

sim_datasets_unnest <- sim_datasets %>%
  unnest(dataset) %>%
  mutate(beta0_mu_delinked = exp(beta0_mu)/(exp(beta0_mu) + 1),
         beta1_mu_delinked = exp(beta0_mu + betaD_mu)/(exp(beta0_mu + betaD_mu) + 1),
         subj_pre_pMem = exp(subj_beta0)/(exp(subj_beta0) + 1),
         subj_post_pMem = exp(subj_betaD + subj_beta0)/(exp(subj_betaD + subj_beta0) + 1),
         subj_pMem_ES = subj_post_pMem - subj_pre_pMem) 

pMem_ES_quantiles <- quantile(sim_datasets_unnest$subj_pMem_ES, c(0.025, 0.975))

plot_grid(
  
  sim_datasets_unnest %>%
  group_by(sim_num) %>%
  sample_n(1) %>%
  ungroup() %>%
  ggplot(aes(x = subj_pre_pMem)) + 
  geom_histogram(binwidth = 0.01, fill = "red", alpha = 0.3) + 
  labs(x = "subj_pre_pMem [prior predictive distribution]",
       subtitle = glue("p(< 0.05) = {sum(sim_datasets_unnest$subj_pre_pMem < 0.05)/length(sim_datasets_unnest$subj_pre_pMem)}\n p(> 0.95) = {sum(sim_datasets_unnest$subj_pre_pMem > 0.95)/length(sim_datasets_unnest$subj_pre_pMem)}"))
  
  ,
  
  sim_datasets_unnest %>%
  group_by(sim_num) %>%
  sample_n(1) %>%
  ungroup() %>%  
  ggplot(aes(x = subj_post_pMem)) + 
  geom_histogram(binwidth = 0.01, fill = "red", alpha = 0.3) + 
  labs(x = "subj_post_pMem [prior predictive distribution]",
       subtitle = glue("p(< 0.05) = {sum(sim_datasets_unnest$subj_post_pMem < 0.05)/length(sim_datasets_unnest$subj_post_pMem)}\n p(> 0.95) = {sum(sim_datasets_unnest$subj_post_pMem > 0.95)/length(sim_datasets_unnest$subj_post_pMem)}"))
  
  ,
  
  sim_datasets_unnest %>%
  group_by(sim_num) %>%
  sample_n(1) %>%
  ungroup() %>%  
  ggplot(aes(x = subj_pMem_ES)) + 
  geom_histogram(binwidth = 0.01, fill = "red", alpha = 0.7) + 
  geom_vline(xintercept = pMem_ES_quantiles, linetype = "dashed") + 
  labs(x = "subj_pMem_ES [prior predictive distribution], (5%, 95%) quantile lines",
       subtitle = glue("p(< -0.8) = {sum(sim_datasets_unnest$subj_pMem_ES < -0.8)/length(sim_datasets_unnest$subj_pMem_ES)}\n p(> 0.8) = {sum(sim_datasets_unnest$subj_pMem_ES > 0.80)/length(sim_datasets_unnest$subj_pMem_ES)}"))
  
  ,
  
  ncol = 1
)

Calculate min and max subject pre, post, and pMem effect size in each simulation.

sim_subj_extremes <- sim_datasets %>% 
  unnest(dataset) %>%
  mutate(subj_beta1 = subj_beta0 + subj_betaD, 
         subj_beta0_delinked = exp(subj_beta0)/(exp(subj_beta0) + 1), 
         subj_beta1_delinked = exp(subj_beta0 + subj_betaD)/(exp(subj_beta0 + subj_betaD) + 1), 
         subj_pMem_effect = subj_beta1_delinked - subj_beta0_delinked ) %>%
  group_by(sim_num) %>%
  summarize_at(vars(subj_beta0_delinked, subj_beta1_delinked, subj_pMem_effect), list(max = max, min = min)) 

Across-sim max pMem

plot_grid(

  #What is the max subject pre condition value in each dataset
  sim_subj_extremes %>%
  ggplot() + 
  geom_histogram(aes(x = subj_beta0_delinked_max, fill = "red", alpha = 0.3), binwidth = 0.02) +
  theme(legend.position = "none") + 
  labs(x = "pre condition: max subj pMem per sim [subj_beta0_delinked_max]",
       subtitle = glue("p(< 0.05) = {sum(sim_subj_extremes$subj_beta0_delinked_max < 0.05)/length(sim_subj_extremes$subj_beta0_delinked_max)}\n p(> 0.95) = {sum(sim_subj_extremes$subj_beta0_delinked_max > 0.95)/length(sim_subj_extremes$subj_beta0_delinked_max)}"))
  
  ,

  #What is the max subject post condition value in each dataset
  sim_subj_extremes %>%
  ggplot() + 
  geom_histogram(aes(x = subj_beta1_delinked_max, fill = "red", alpha = 0.3), binwidth = 0.02) + 
  theme(legend.position = "none") + 
  labs(x = "post condition: max subj pMem per sim [subj_beta1_delinked_max]",
       subtitle = glue("p(< 0.05) = {sum(sim_subj_extremes$subj_beta1_delinked_max < 0.05)/length(sim_subj_extremes$subj_beta1_delinked_max)}\n p(>0.95) = {sum(sim_subj_extremes$subj_beta1_delinked_max > 0.95)/length(sim_subj_extremes$subj_beta1_delinked_max)}"))

  ,
  ncol =1,
  align = 'v'

)

Across-sim min pMem

plot_grid(

  #What is the min subject pre condition value in each dataset
  sim_subj_extremes %>%
  ggplot() + 
  geom_histogram(aes(x = subj_beta0_delinked_min, fill = "red", alpha = 0.3), binwidth = 0.02) +
  theme(legend.position = "none") + 
  labs(x = "pre condition: min subj pMem per sim [subj_beta0_delinked_min]",
       subtitle = glue("p(< 0.05) = {sum(sim_subj_extremes$subj_beta0_delinked_min < 0.05)/length(sim_subj_extremes$subj_beta0_delinked_min)}\n p(> 0.95) = {sum(sim_subj_extremes$subj_beta0_delinked_min > 0.95)/length(sim_subj_extremes$subj_beta0_delinked_min)}"))
  
  ,

  #What is the min subject post condition value in each dataset
  sim_subj_extremes %>%
  ggplot() + 
  geom_histogram(aes(x = subj_beta1_delinked_min, fill = "red", alpha = 0.3), binwidth = 0.02) + 
  theme(legend.position = "none") + 
  labs(x = "post condition: min subj pMem per sim [subj_beta1_delinked_min]",
       subtitle = glue("p(< 0.05) = {sum(sim_subj_extremes$subj_beta1_delinked_min < 0.05)/length(sim_subj_extremes$subj_beta1_delinked_min)}\n p(>0.95) = {sum(sim_subj_extremes$subj_beta1_delinked_min > 0.95)/length(sim_subj_extremes$subj_beta1_delinked_min)}"))

  ,
  ncol =1,
  align = 'v'

)

Across-sim max+min pMem effect size

#What is the most extreme change from pre to post in a subject

min_plot <- sim_subj_extremes %>%
  mutate(subj_pMem_effect_min = if_else(subj_pMem_effect_min > 1 , 1, subj_pMem_effect_min)) %>%
  mutate(subj_pMem_effect_min = if_else(subj_pMem_effect_min < -1 , -1, subj_pMem_effect_min)) %>%
  ggplot() + 
  geom_histogram(aes(x = subj_pMem_effect_min, fill = "red", alpha = 0.3), binwidth = 0.03) +
  theme(legend.position = "none") + 
  labs(x = "min subj pMem effect per sim \n[min(subj_beta1_delinked - subj_beta0_delinked)]",
       subtitle = glue("p(<-0.8) = {sum(sim_subj_extremes$subj_pMem_effect_min < -0.8)/length(sim_subj_extremes$subj_pMem_effect_min)}\n p(>0.8) = {sum(sim_subj_extremes$subj_pMem_effect_min > 0.8)/length(sim_subj_extremes$subj_pMem_effect_min)}")) + 
  xlim(c(-1, 1))

#What is the most extreme subject post condition value in each dataset
max_plot <- sim_subj_extremes %>%
  mutate(subj_pMem_effect_max = if_else(subj_pMem_effect_max > 1 , 1, subj_pMem_effect_max)) %>%
  mutate(subj_pMem_effect_max = if_else(subj_pMem_effect_max < -1 , -1, subj_pMem_effect_max)) %>%
  ggplot() + 
  geom_histogram(aes(x = subj_pMem_effect_max, fill = "red", alpha = 0.3), binwidth = 0.03) +
  theme(legend.position = "none") + 
  labs(x = "max subj pMem effect per sim \n[max(subj_beta1_delinked - subj_beta0_delinked)]",
       subtitle = glue("p(<-0.8) = {sum(sim_subj_extremes$subj_pMem_effect_max < -0.8)/length(sim_subj_extremes$subj_pMem_effect_max)}\n p(>0.8) = {sum(sim_subj_extremes$subj_pMem_effect_max > 0.8)/length(sim_subj_extremes$subj_pMem_effect_max)}")) + 
    xlim(c(-1, 1))

plot_grid(min_plot, max_plot, ncol =1, align = 'v')

## Warning: Removed 2 rows containing missing values (geom_bar).

## Warning: Removed 2 rows containing missing values (geom_bar).

* Notes

---

Joint prior on pre condition + effect size

joint_pre_plot <- sim_datasets_unnest %>% 
  group_by(sim_num) %>%
  sample_n(1) %>%
  ungroup() %>%
  ggplot(aes(y = exp(subj_alpha0), x = exp(subj_beta0)/(exp(subj_beta0) + 1))) +
    geom_point() +
    labs(x = 'pMem, pre', y = 'circSD, pre')

plot_grid(
  joint_pre_plot,
  ncol = 1,
  align = 'v'
)

joint_ES_plot <- sim_datasets_unnest %>% 
  group_by(sim_num) %>%
  sample_n(1) %>%
  ungroup() %>%
  mutate(subj_pMem_ES = exp(subj_beta0 + subj_betaD)/(exp(subj_beta0 + subj_betaD) + 1) - exp(subj_beta0)/(exp(subj_beta0) + 1),
         subj_circSD_ES = exp(subj_alpha0 + subj_alphaD) - exp(subj_alpha0)) %>%
  ggplot(aes(x = subj_pMem_ES, y = subj_circSD_ES)) +
    geom_point() +
    geom_vline(xintercept = 0, linetype = 'dashed') + 
    geom_hline(yintercept = 0, linetype = 'dashed')
  
plot_grid(
  joint_ES_plot,
  joint_ES_plot + ylim(c(-200, 200)) + labs(subtitle = "zoom in"),
  ncol = 1,
  align = 'v'
)

## Warning: Removed 53 rows containing missing values (geom_point).

---

Prior predicitive distribution at the observation level, per condition

(based on simulated obs from each dataset)

again only using one subject from each simulated dataset.

#######################################################
# calculate histogram quantile mats from each condition

sim_subj_obs_hist_count <- function(dataset, condition = 0){
  
  dataset_obs <- dataset %>% 
    sample_n(1) %>%
    unnest(subj_obs) %>%
    filter(stimulation == condition) %>%
    select(obs_degree)
  
  breaks <- seq(-180, 180, 5)
  
  bincount <- hist(dataset_obs$obs_degree, breaks = breaks, plot = FALSE)$counts
  
  bincount_names <- glue("c{breaks[-1]}")
  
  names(bincount) <- bincount_names
  bincount_df <- data.frame(as.list(bincount))

  return(bincount_df)
  
}

make_quantmat <- function(sim_datasets, condition = 0){

  bincounts <- sim_datasets %>% 
  select(dataset) %>% 
  mutate(subj_hist_counts = map(dataset, sim_subj_obs_hist_count, condition)) %>% 
  select(-dataset) %>% 
  unnest(subj_hist_counts) %>%
  as_tibble()


  xvals <- seq(-177.5, 177.5, 5)
  probs <- seq(0.1,0.9,0.1)

  quantmat <- as.data.frame(matrix(NA, nrow=ncol(bincounts), ncol=length(probs)))
  names(quantmat) <- paste0("p",probs)

  quantmat <- cbind(quantmat, xvals)

  for (iQuant in 1:length(probs)){
   quantmat[,paste0("p",probs[iQuant])] <- as.numeric(summarise_all(bincounts, ~quantile(., probs[iQuant])))
  }
    
  return(quantmat)
}

quantmat_cond0 <- make_quantmat(sim_datasets, 0)
quantmat_cond1 <- make_quantmat(sim_datasets, 1)


#######################################################
# calculate ecdf quantile mats from each condition

# unnest sim_datasets, using only 1 subj/dataset
unnested <- 
  sim_datasets %>%
  unnest(dataset) %>%
  group_by(sim_num) %>%
  sample_n(1) %>%
  ungroup() %>%
  unnest(subj_obs)

# calc quantiles mat for pre condition
ecdf_res_stim0 <- 
  unnested %>% 
  filter(stimulation == 0) %>%
  group_by(sim_num) %>% 
  group_map(~ecdf(.$obs_degree )(seq(-180, 180, 1)))

stim0_ecdf_quantiles <- bind_cols(
  tibble(x_val = seq(-180, 180, 1)), 
  as_tibble(colQuantiles(do.call(rbind, ecdf_res_stim0), probs = c(0.95, 0.5, 0.05 )))
  )

# calc quantiles mat for post condition
ecdf_res_stim1 <- 
  unnested %>% 
  filter(stimulation == 1) %>%
  group_by(sim_num) %>% 
  group_map(~ecdf(.$obs_degree )(seq(-180, 180, 1)))

stim1_ecdf_quantiles <- bind_cols(
  tibble(x_val = seq(-180, 180, 1)), 
  as_tibble(colQuantiles(do.call(rbind, ecdf_res_stim1), probs = c(0.95, 0.5, 0.05 )))
  )

# blues
b_light <- "#8C9BC4"
b_light_highlight <- "#A0ADCE"
b_mid   <- "#546BA9"
b_mid_highlight   <- "#7385B8"
b_dark  <- "#002381"
b_dark_highlight  <- "#2E4B97"

#betancourt reds
r_light <- "#DCBCBC"
r_light_highlight <- "#C79999"
r_mid   <- "#B97C7C"
r_mid_highlight   <- "#A25050"
r_dark  <- "#8F2727"
r_dark_highlight  <- "#7C0000"


#######################################################
# plot histogram(density) per condition

ggplot(quantmat_cond0, aes(x = xvals)) + 
  geom_ribbon(aes(ymax = p0.9, ymin = p0.1), fill = r_light, alpha = 0.4) + 
  geom_line(aes(y = p0.5), color = r_dark, size = 1) + 
  geom_ribbon(data = quantmat_cond1, aes(ymax = p0.9, ymin = p0.1), fill = b_light, alpha = 0.4) + 
  geom_line(data = quantmat_cond1, aes(y = p0.5), color = b_dark, size = 1) + 
  scale_x_continuous(breaks=pretty_breaks(10)) + 
  labs(x = "error (degrees) [red = pre, blue = post]", 
       y = "count +/- quantile", 
       subtitle = glue("per-condition prior pred dist (median line, 90% interval over {nrow(sim_datasets)} sim datasets)\n({nobs_per_cond_sim} samples/cond, per subj-level draw, per group-level mean + sd draw)")) + 
  theme_cowplot()

#######################################################
# plot ecdf per condition

ggplot() +
  geom_ribbon(data = stim0_ecdf_quantiles, aes(x = x_val, ymax = `95%`, ymin = `5%`), fill = "red", alpha = 0.3) + 
  geom_line(data = stim0_ecdf_quantiles, aes(x = x_val, y = `50%`), color = "red", size = 1) +
  geom_ribbon(data = stim1_ecdf_quantiles, aes(x = x_val, ymax = `95%`, ymin = `5%`), fill = "blue", alpha = 0.3) + 
  geom_line(data = stim1_ecdf_quantiles, aes(x = x_val, y = `50%`), color = "blue", size = 1) + 
  scale_x_continuous(breaks=pretty_breaks(10)) + 
  geom_hline(yintercept = seq(0, 1, 0.25), linetype = "dashed", alpha = 0.2) +
  labs(x = "error (degrees) [red = pre, blue = post]", 
       y = "cumulative prob.", 
       subtitle = glue("per-condition prior pred cdf (median line, 90% interval over {nrow(sim_datasets)} sim datasets) \n({nobs_per_cond_sim} samples/cond, per subj-level draw, per group-level mean + sd draw"))

plot_grid(          
                                                                  
  ggplot(quantmat_cond0, aes(x = xvals)) + 
    geom_ribbon(aes(ymax = p0.9, ymin = p0.1), fill = c_light) + 
    geom_ribbon(aes(ymax = p0.8, ymin = p0.2), fill = c_light_highlight) + 
    geom_ribbon(aes(ymax = p0.7, ymin = p0.3), fill = c_mid) + 
    geom_ribbon(aes(ymax = p0.6, ymin = p0.4), fill = c_mid_highlight) + 
    geom_line(aes(y = p0.5), color = c_dark, size = 1) + 
    scale_x_continuous(breaks=pretty_breaks(10)) + 
    coord_cartesian(ylim = c(0, 150)) + 
    labs(x = "error (degrees)", y = "count +/- quantile", subtitle = "without stimulation")
  ,

  ggplot(quantmat_cond1, aes(x = xvals)) + 
    geom_ribbon(aes(ymax = p0.9, ymin = p0.1), fill = c_light) + 
    geom_ribbon(aes(ymax = p0.8, ymin = p0.2), fill = c_light_highlight) + 
    geom_ribbon(aes(ymax = p0.7, ymin = p0.3), fill = c_mid) + 
    geom_ribbon(aes(ymax = p0.6, ymin = p0.4), fill = c_mid_highlight) + 
    geom_line(aes(y = p0.5), color = c_dark, size = 1) + 
    scale_x_continuous(breaks=pretty_breaks(10)) +
    coord_cartesian(ylim = c(0, 150)) + 
    labs(x = "error (degrees)", y = "count +/- quantile", subtitle = "with stimulation")
  ,
  
  sim_datasets %>%
    sample_n(1) %>%
    unnest(dataset) %>%
    unnest(subj_obs) %>% 
    filter(stimulation == sample(c(0,1), 1)) %T>%
    print() %>%
    ggplot(aes(x = obs_degree)) + 
    geom_density() + 
    labs(subtitle = "correctness check: random simulation, random condition") + 
    scale_x_continuous(breaks=pretty_breaks(10))
  ,
  
  ncol = 1,
  align = "v"
)

* Notes

No effect predicted in this prior.